Inner dialogue. Internal thought. Interior monologue. Internal speech. Whatever you call it, this internal thought process is as important as regular dialogue, character arc, and narrative arc in helping your reader understand your main character at an intimate level. It also serves to move your story forward and keep your readers deeply connected.
Unlike the one- or two-dimensional characters you see in movies and on television, when using inner dialogue in your narrative, it helps you present a much more nuanced and three-dimensional character. And since most stories are character driven, you really need to add that inner dialogue in.